<h2>Problem 235</h2>
<div style="color:#666;font-size:80%;">07 March 2009</div><br />
<div class="problem_content">
<p>
Given is the arithmetic-geometric sequence u(<var>k</var>) = (900-3<var>k</var>)<var>r</var><img src="" style="display:none;" alt="^(" /><sup><var>k</var>-1</sup><img src="" style="display:none;" alt=")" />.<br />
Let s(<var>n</var>) = &Sigma;<img src="" style="display:none;" alt="_(" /><sub><var>k</var>=1...<var>n</var></sub><img src="" style="display:none;" alt=")" />u(<var>k</var>).
</p>
<p>
Find the value of <var>r</var> for which s(5000) = -600,000,000,000.
</p>
<p>
Give your answer rounded to 12 places behind the decimal point.
</p>



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